Translation invariant realizability problem on the d-dimensional lattice: an explicit constructionKuna, T., Caglioti, E. and Infusino, M. (2016) Translation invariant realizability problem on the d-dimensional lattice: an explicit construction. Electronic Communications in Probability, 21. 45. ISSN 1083-589X
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1214/16-ECP4620 Abstract/SummaryWe consider a particular instance of the truncated realizability problem on the d−dimensional lattice. Namely, given two functions ρ1(i) and ρ2(i,j) non-negative and symmetric on Zd, we ask whether they are the first two correlation functions of a translation invariant point process. We provide an explicit construction of such a realizing process for any d ≥ 2 when the radial distribution has a specific form. We also derive from this construction a lower bound for the maximal realizable density and compare it with the already known lower bounds.
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